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Simplifying 2p(p + 2) + -3p(2p + -3) = 0 Reorder the terms: 2p(2 + p) + -3p(2p + -3) = 0 (2 * 2p + p * 2p) + -3p(2p + -3) = 0 (4p + 2p2) + -3p(2p + -3) = 0 Reorder the terms: 4p + 2p2 + -3p(-3 + 2p) = 0 4p + 2p2 + (-3 * -3p + 2p * -3p) = 0 4p + 2p2 + (9p + -6p2) = 0 Reorder the terms: 4p + 9p + 2p2 + -6p2 = 0 Combine like terms: 4p + 9p = 13p 13p + 2p2 + -6p2 = 0 Combine like terms: 2p2 + -6p2 = -4p2 13p + -4p2 = 0 Solving 13p + -4p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(13 + -4p) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(13 + -4p)' equal to zero and attempt to solve: Simplifying 13 + -4p = 0 Solving 13 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -4p = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -4p = 0 + -13 -4p = 0 + -13 Combine like terms: 0 + -13 = -13 -4p = -13 Divide each side by '-4'. p = 3.25 Simplifying p = 3.25Solution
p = {0, 3.25}
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